Graph G(x)=5|x-3 - Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Graph g(x)=5|x-3| Step 1Find the absolute value vertex. In this case, the vertex for is .Tap for more steps...Step 1.1To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .Step 1.2Add to both sides of the equation.Step 1.3Replace the variable with in the expression.Step 1.4Simplify .Tap for more steps...Step 1.4.1Subtract from .Step 1.4.2The absolute value is the distance between a number and zero. The distance between and is .Step 1.4.3Multiply by .Step 1.5The absolute value vertex is .Step 2The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.Interval Notation:Set-Builder Notation:Step 3For each value, there is one value. Select a few values from the domain. It would be more useful to select the values so that they are around the value of the absolute value vertex.Tap for more steps...Step 3.1Substitute the value into . In this case, the point is .Tap for more steps...Step 3.1.1Replace the variable with in the expression.Step 3.1.2Simplify the result.Tap for more steps...Step 3.1.2.1Subtract from .Step 3.1.2.2The absolute value is the distance between a number and zero. The distance between and is .Step 3.1.2.3Multiply by .Step 3.1.2.4The final answer is .Step 3.2Substitute the value into . In this case, the point is .Tap for more steps...Step 3.2.1Replace the variable with in the expression.Step 3.2.2Simplify the result.Tap for more steps...Step 3.2.2.1Subtract from .Step 3.2.2.2The absolute value is the distance between a number and zero. The distance between and is .Step 3.2.2.3Multiply by .Step 3.2.2.4The final answer is .Step 3.3Substitute the value into . In this case, the point is .Tap for more steps...Step 3.3.1Replace the variable with in the expression.Step 3.3.2Simplify the result.Tap for more steps...Step 3.3.2.1Subtract from .Step 3.3.2.2The absolute value is the distance between a number and zero. The distance between and is .Step 3.3.2.3Multiply by .Step 3.3.2.4The final answer is .Step 3.4The absolute value can be graphed using the points around the vertex Step 4

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